Abstract

We consider the stationary Gierer-Meinhardt system in ?2: ?A - A + A2H = 0 in ?2, ?H - ? 2 H + A2 = 0 in ?2, A, H > 0; A, H ? 0 as |x| ? + ?. We construct multi-bump ground-state solutions for this system for all sufficiently small ?. The centers of these bumps are located at the vertices of a regular polygon, while the bumps resemble, after a suitable scaling in their A-coordinate, the unique radially symmetric solution of ?w - w + w2 = 0 in ?2, 0 < w (y) ? 0 as |y| ? ?. A similar construction is made for vertices of two concentric polygons and a general procedure for detection of organized finite patterns is suggested. © 2003 Éditions scientifiques et médicales Elsevier SAS.